Hi, welcome to the forum
If the cigarette lighter element heats up the socket is receiving power. a 15 amp or 20 amp fuse should not alter this. Most cars use a 15 amp fuse but some use a 20 amp fuse. Its best to change it to 15 amps if thats whats recommended.
If the cigarette lighter has been used to light cigarettes, any time in the last 20 years, its quite possible the the inside of the socket has become dirty and or corroded, giving poor electrical contact. It may be good enough for the cigarette lighter device, which are typically made to original manufacturers quality, but the plugs on devices, and the 5v USB adapters used to power many devices are often quite cheaply made and might not be making good electrical contact. Have you tried different adapter, or confirmed the adapter, or the individual devices work properly in a different car?
I would suggest cleaning the contacts in the socket (whilst the ignition is off. ) The centre contact at the bottom and also the metal edges . There are you tube videos explaining how. Also if you are plugging in a plug that feeds an individual device, or feeds an adapter with 2 or more lighter sockets check the fuse in the plug itself .(Not the car fuse) The plugs often unscrew and you will find an in-line fuse inside . Also check its centre sprung electrode is clean and springing in and out, and that the two side electodes are also clean and springy. Self contained 5v usb adapters may not unscrew in this way or have their own fuse and would need to be replaced if faulty.
If 20 years of cigarette ash (or south african desert dust

) means the socket is not salvageable they are not difficult to replace. I expect there will be how to videos on you tube . Indeed if you are currently using multiple adapters to run multiple devices it might be a good idea to install a second cigarette lighter socket anyway.
Let us know how you get on.